Hii nauna,

You can't call Web Method from User Control.

Create a Web Service and write the web method inside it, then use the web service to make Ajax call.

Refer below sample.

User Control

HTML 

<asp:ListView ID="lvCustomers" runat="server">
    <ItemTemplate>
        <div id="dvhitem">
            <asp:Label ID="lblCustomerId" runat="server" Text='<%#Eval("CustomerId") %>'></asp:Label>
            <asp:Label ID="lblName" runat="server" Text='<%#Eval("Name") %>'></asp:Label>
            <asp:Label ID="lblCountry" runat="server" Text='<%#Eval("Country") %>'></asp:Label>
            <asp:LinkButton ID="lnkComparisionList" runat="server">Save</asp:LinkButton>
        </div>
        <hr />
    </ItemTemplate>
</asp:ListView>

Namespaces

C#

using System.Data;
using System.Configuration;
using System.Data.SqlClient;

Code

protected void Page_Load(object sender, EventArgs e)
{
    if(!this.IsPostBack)
    {
        this.BindListView();
    }
}

private void BindListView()
{
    string constring = ConfigurationManager.ConnectionStrings["constring"].ConnectionString;
    using (SqlConnection con = new SqlConnection(constring))
    {
        using (SqlCommand cmd = new SqlCommand("SELECT * FROM Customers", con))
        {
            using (SqlDataAdapter sda = new SqlDataAdapter(cmd))
            {
                using (DataTable dt = new DataTable())
                {
                    sda.Fill(dt);
                    lvCustomers.DataSource = dt;
                    lvCustomers.DataBind();
                }
            }
        }
    }
}

Web Service

Code

using System;
using System.Collections.Generic;
using System.Linq;
using System.Web;
using System.Web.Services;
using System.Data;
using System.Configuration;
using System.Data.SqlClient;

[WebService(Namespace = "http://tempuri.org/")]
[WebServiceBinding(ConformsTo = WsiProfiles.BasicProfile1_1)]
[System.Web.Script.Services.ScriptService]
public class WebService : System.Web.Services.WebService
{
[WebMethod]
public void Save(string name, string country)
{
    string constring = ConfigurationManager.ConnectionStrings["constring"].ConnectionString;
    using (SqlConnection con = new SqlConnection(constring))
    {
        using (SqlCommand cmd = new SqlCommand("INSERT INTO Customers VALUES(@Name, @Country)", con))
        {
            cmd.Parameters.AddWithValue("@Name", name);
            cmd.Parameters.AddWithValue("@Country", country);
            con.Open();
            cmd.ExecuteNonQuery();
            con.Close();
        }
    }
}
}

Default

HTML

<uc:WebMethod runat="server" />
<script type="text/javascript" src="https://ajax.googleapis.com/ajax/libs/jquery/1.8.3/jquery.min.js"></script>
<script type="text/javascript">
    $(function () {
        $('[id*=lnkComparisionList]').on('click', function () {
            var item = $(this).closest('[id*=dvhitem]');
            var obj = {};
            obj.name = $(item).find('[id*=lblName]').html();
            obj.country = $(item).find('[id*=lblCountry]').html();
            $.ajax({
                type: "POST",
                url: "WebService.asmx/Save",
                data: JSON.stringify(obj),
                contentType: "application/json; charset=utf-8",
                dataType: "json",
                success: function (response) {

                },
                failure: function (response) {
                    alert(response.responseText);
                },
                error: function (response) {
                    alert(response.responseText);
                }
            });

            return false;
        });
    });
</script>

Screenshot